Since the work of John Cook Wilson (1926) several analyses have been proposed for the distinction between 'positive' and 'negative' properties (cf. Ayer, 1952; Gale, 1970; Hirsch, 1989). These analyses have relied on the 'specification', the 'incompatibility', or the 'strength' of properties. Some have proposed, for example, that negative properties are those that do not specify other negative properties, or those that are not incompatible with other negative properties, or those that have 'less strength' that their complementary properties. Many difficulties affect these analyses. Most of them rely on the concept of the 'quality' of a property, i. e., the fact that a property is either positive or negative. Many think that relying on this concept could be circular. Other analyses work under the supposition that there are structures of subordination, like genera-species or determinables-determinates, that seem to presuppose positive properties. David Hommen has proposed another analysis (2018) in terms of 'minimal' or 'maximal' properties. According to Hommen, a property is negative if and only if it has simple minimals in structures under certain conditions. This work discusses and criticizes Hommen's proposal. It appears that it requires several qualifications. Even under them, nevertheless, it has fatal problems.